Has your ex pushed for the overnights?
My XH left when my DC were 1 and 3. Now 15 and 12 (soon 13). He's had the younger for two overnights so far. Lots of talk and promises over the years but it mutually didn't work out very well when it finally happened. Nothing catastrophic just lack of sleep and not quite the fun thing that he'd conjured up having a young child overnight to be. Elder is Autistic and more than a few hours is complex enough.
In theory when They're gone you enjoy a night off, have a nice meal and a few drinks etc. In reality you check your mobile every 10 seconds like a nervous twitch, ask people to ring off if they call incase your DC needs you, sleep with phone on your pillow, don't drink incase you're needed in an emergency. Then to top it off, they come home a bit tired but have survived and you further beat yourself up that you didn't enjoy your time to relax.
The next time they're out you might make it out the house for a coffee or supermarket shop, sleep with your mobile on the bedside table. Talk on the phone for a few moments. You're more prepared for an easy day on their return because you know they'll be a bit tired. And so it continues.
A decade goes by. I don't relish them being out, I still feel slightly anxious as I know that it doesn't always go brilliantly (this is just days mind in our case) but I know they'll be coming back, I don't fear for their safety in the same way, they are older and can call me if there are problems.
We stayed out the courts and have gone with our and the children's needs. Every other weekend and a night midweek formula doesn't fit all. If you can keep a communication line open and he can be honest about whether the sleepover works that's great. It's not easy but it's got to be better than handing over every penny you have to solicitors.